aliki mavromoustaki
Welcome!
I am a CAM assistant adjunct professor in the Department of Mathematics at UCLA in Prof. Andrea Bertozzi's group.
I completed my Ph.D in the Department of Chemical Engineering at Imperial College in February 2011, in the field of theoretical and computational fluid dynamics.
Research interests | Past projects | Current projects
Research interests
My current research interests are in the application of analytical, semi-analytical and numerical methods to the solution of problems in interfacial fluid mechanics. A notable exemplar of these problems is the dynamics of thin film in the presence of numerous complexities that include:
- the presence of two (or more), immiscible fluid phases;
- particles;
- surface active agents (surfactant);
- non-Newtonian effects.
Due to these complexities, the thin films are driven by Marangoni stresses (due to gradients in surfactant concentration), gravitational forces, and particle sedimentation. As discussed below, the films exhibit complex dynamics, such as the formation of travelling waves, which can be unstable to spanwise perturbations that lead to the development of fingering instabilities. The techniques I use to study the abovementioned problems are:
- asymptotic methods;
- stability theory (linear stability and transient growth analyses);
- entropy-flux analysis;
- numerical methods: finite-difference, finite-element-based methods, operator-splitting methods (e.g. alternating direction implicit [ADI] techniques).
This work has numerous practical applications that range from coating flow technology, to the displacement of oil and water in enhanced oil recovery.
Past projects
My work in the area of two-fluid, pressure-driven flows in inclined channels exploits the channel slenderness and employs lubrication theory to derive a single, two-dimensional, highly nonlinear evolution equation for the interface. Using an entropy-flux analysis, I uncovered the formation of travelling-waves, whose structure depends on the flow rates of the two fluids occupying the channel, their height, density and viscosity ratios, and the flow configuration (whether co- or counter-current). The travelling waves include compressive Lax-shocks, pairs of Lax and under-compressive shocks, and rarefaction waves. Flows characterised by unstably-stratified layers are accompanied by the formation of propagating, large-amplitude interfacial waves, which are not shock-like in nature. A transient growth analysis of the linearised equation reveals that increasing the density and/or the viscosity of the upper layer, and/or increasing the counter-current nature of the flow configuration exerts a stabilising influence. Single Lax-shocks and the trailing Lax-shocks in Lax-undercompressive double-shocks are unstable to finger formation; undercompressive shocks and rarefaction waves are stable. In unstably-stratified cases, increasing the channel inclination away from verticality, such
that a denser upper layer overhangs a less dense lower one, is found to be destabilising. ADI is used to probe the stability in the nonlinear regime.
My work on surfactant-driven thin films involved an examination of films climbing up an inclined plane using lubrication theory. Here, an interface equation is coupled to convective-diffusion equations for the surfactant species, which are allowed to exist in the bulk as both monomers and aggregates (or 'micelles', as they are commonly called in surface and colloid science), and at the interface. Two configurations were examined: a constant volume (essentially, a droplet deposited on the inclined wall), and a constant flux (constant 'feeding' of fluid and surfactant at the flow origin). In both configurations, one-dimensional solutions show the development of a front that spreads up the substrate against the direction of gravity whereby the leading edge of the front follows a power-law as a function of time. I have also studied the linear and nonlinear stability of the spreading film in both configurations using transient growth and ADI. These methods indicate that the spreading films are unstable to fingering and help uncover the mechanism underlying the surfactant-driven enhancement of this phenomenon.
Click here for Ph.D (Imperial College 2011) thesis.
Current projects
My work on the dynamics of thin, particle-laden films flowing down inclined planes involves the derivation of an interface equation coupled to a convective-diffusion equation for the particle concentration. This coupled system accounts for gravitational, viscous, and capillary effects, in addition to hindered-settling, and shear-induced migration. This work is currently being carried out in collaboration with Prof. Andrea Bertozzi, Dr. Dirk Peschka, Dr. Nebo Murisic and Dr. Sungyon Lee.
The Research Experience for Undergraduates (REU) is an intense research program, in which undergraduate students are offered the opportunity to conduct research in Applied and Computational Mathematics. The research topics previously studied include crime modelling, medical imaging, experiments and modelling of fluid dynamics systems, image processing, robotic testbed swarms, plant/ecology population modelling and social networking.
A list of the planned projects for summer 2013 can be found here.
Program details
Program duration: 17 June - 9 August, 2013
Application deadline: 12 February 2013
Click here for further information and to apply.
Journal papers | Conference talks & workshops
Journal papers
- Dynamics of a climbing surfactant-laden film I: Base-state flow.
Mavromoustaki A, Matar OK, Craster RV
Accepted for publication in J Colloid Interface Sci., 2012 - Dynamics of a climbing surfactant-laden film II: Stability.
Mavromoustaki A, Matar OK, Craster RV
J Colloid Interface Sci, 2011 - Shock-wave solutions in two-layer channel flow. Part II. Linear and nonlinear stability.
Mavromoustaki A, Matar OK, Craster RV
Phys. Fluids 23, 112101, 2011 - Shock-wave solutions in two-layer channel flow. Part I. One-dimensional flows.
Mavromoustaki A, Matar OK, Craster RV
Phys. Fluids 22, 112102, 2010
Conference talks & workshops
- Applied Math Seminar, Claremont Center for the Mathematical Sciences, Claremont, CA, USA (March 2012)
- A. Mavromoustaki and A. Bertozzi, "Dynamics of particle-laden, thin-film flow ".
- 64th Annual Meeting of the APS Division of fluid dynamics, Baltimore, MD, USA (November 2011)
- W. Rosenthal, P. Latterman, S. Hill, P. David, M. Mata, A. Mavromoustaki and A. Bertozzi, "An experimental study of gravity-driven thin-film flow with buoyant particles".
- P. David, S. Hill, P. Latterman, W. Rosenthal, A. Mavromoustaki, M. Mata and A. Bertozzi, "Theoretical challenges in modeling gravity-driven thin-film flow with buoyant particles".
- Chemical Engineering Ph.D Research Symposium, Imperial College, London, UK (March 2010)
- A. Mavromoustaki, "Modelling of two-layer flows".
- 63rd Annual Meeting of the APS Division of fluid dynamics, Long Beach, CA, USA (November 2010)
- A. Mavromoustaki, O. K. Matar and R. V. Craster, "Shock-wave solutions and their stability in two-layer channel flow".
- Attended Workshop on "Small-scale hydrodynamics: microfluidics and thin films", Banff, AB, Canada (February 2010).
- 62nd Annual Meeting of the APS Division of fluid dynamics, Minneapolis, MN, USA (November 2009)
- A. Mavromoustaki, L. O'Naraigh and O. K. Matar, "Dynamics and stability of turbulent falling films".
SPRING 2013:
Math 33B - Differential equations
FALL 2011, SPRING 2012:
Math 135 - Ordinary differential equations
Enrolled students can log on CCLE with their credentials to access the course sites.
Aliki Mavromoustaki
CAM Assistant Adjunct Professor
Department of Mathematics
University of California, Los Angeles
Postal Address:
Box 951555
Los Angeles, CA 90095-1555
Office Location: 7354 Math Sciences Building
Email Address: am503@math.ucla.edu
Office Phone: +1-310-825-8525